Columbus State University
1999-2000 Academic Catalog

Course Descriptions

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MATH - Mathematics

MATH 0097. Developmental Math 1 (4-0-(4) Review of basic mathematics and introductory algebra with emphasis on applications, including linear functions and related topics. Non-degree credit.

MATH 0098. Developmental Math 2 (4-0-(4) Prerequisite: MATH 0097 or required COMPASS score. Review of essential topics of basic algebra with emphasis on applications, including linear and quadratic functions and related topics. Non-degree credit.

MATH 1101. Mathematical Modeling (3-0-3) Prerequisite: High School Algebra 2 or its equivalent. This course is an introduction to mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, supported by the use of appropriate technology, and on effective communication of quantitative concepts and results.

MATH 1111. College Algebra (3-0-3) Prerequisites: Satisfactory Mathematics Placement Test score and High School Algebra 2. This course is a functional approach to algebra that incorporates the use of appropriate technology. Emphasis will be placed on the study of functions, and their graphs, inequalities, and linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions. Appropriate applications will be included.

MATH 1112. Trigonometry with Analytical Geometry (3-0-3) Circular functions, solutions of triangles, trigonometric identities and equations, graphs of trigonometric functions, Law of Sines, Law of Cosines, applications, vectors, complex numbers, Euler’s formula, DeMoivre’s theorem, and conic sections.

MATH 1113. Pre-Calculus (3-0-3) This course is designed to prepare students for calculus, physics, and related technical subjects. Topics include an intensive study of algebraic and transcendental functions accompanied by analytic geometry.

MATH 1125. Applied Calculus (3-0-3) Prerequisite: MATH 1111 or MATH 1113. Introduction to limits and continuity, differential calculus of algebraic, exponential, and logarithmic functions and partial derivatives; introduction to integration and qualitative behavior of differential equations. Applications in the fields of the behavioral, biological, and managerial sciences are included.

MATH 1131. Calculus with Analytic Geometry 1 (4-0-4) Prerequisite: MATH 1112 or MATH 1113. Topics include analytic geometry, introduction to limits and derivatives, computation and application of derivatives, integrals, exponential and logarithmic functions.

MATH 1132. Calculus with Analytic Geometry 2 (4-0-4) Prerequisite: MATH 1131. Topics include improper integrals, infinite series, techniques of integration, and applications of integration.

MATH 1227. Introductory Statistics (2-3-3) Prerequisite: High School Algebra 2 or its equivalent. Survey of modern statistical methods applicable to behavioral, biological, health and managerial sciences, and education. Organization and analysis of data, probability distributions, sampling distributions, point estimation, confidence interval, hypothesis testing, and regression analysis.

MATH 1265. Computer-Assisted Problem Solving (2-3-3) Prerequisite or Co-requisites: MATH 1125 or MATH 1131. Problem solving using contemporary technology such as graphing calculators, spread sheets, and computer algebra systems. Topics may include interpolation; linear regression; elementary differential models; and an introduction to the fundamentals of computer algebra systems, including manipulation of lists, sets, data structures, functions, plots, and program control structures.

MATH 2115. Introduction to Linear Algebra (3-0-3) Prerequisite or Co-requisite: MATH 1132. Systems of linear equations, matrix algebra, vector spaces, bases for a vector space, linear transformations, eigenvalues and eigenvectors, and matrix decompositions.

MATH 2135. Calculus with Analytic Geometry 3 (4-0-4) Prerequisite: MATH 1132. Topics include real valued functions of several variables, differential calculus of functions of several variables, multiple integration, vector field theory, Green’s Theorem, Divergence Theorem, and Stokes’ Theorem.

MATH 2155. Foundations for Advanced Mathematics (3-0-3) Prerequisite: MATH 1132. Topics include fundamentals of logic, techniques of proof, sets and relations, well ordering and mathematical induction, and functions.

MATH 2175. Introduction to Probability (3-0-3) Prerequisite: MATH 1132. Topics include counting techniques, discrete and continuous random variables, discrete, continuous and multivariate probability distributions, and functions of random variables. Appropriate uses of technology will be implemented to analyze data and to simulate random variables from specified probability distributions. Applications of probability.

MATH 3107. Differential Equations (3-0-3) Prerequisite: MATH 1132 and MATH 2115. Analytic, qualitative, and numerical techniques for ordinary differential equations. Modeling and applications. Eigenvalue method and matrix exponential for solving linear systems. Use of appropriate software and technology.

MATH 3125. Discrete Mathematics (3-0-3) Prerequisites: MATH 1132 and CPSC 1301. Review of set algebra including mapping and relations. Counting methods, permutations, combinations, and recurrence relations. Elements of the theory of directed and undirected graphs. Applications of trees and sorting algorithms.

MATH 4555. Selected Topics in Mathematics for Teachers (3-0-3) Prerequisites: MATH 1101 and MATH 1113. Topics will be suitable for elementary and middle school teachers. Mathematics majors may not receive credit for this course.

MATH 4795. Senior Seminar in Mathematics (2-0-2) Prerequisites: MATH 2155 and Senior Standing. Readings and presentations in selected topics in mathematics. May be repeated for credit.

MATH 5111. Introduction to Abstract Algebra 1 (3-0-3) Prerequisite: MATH 2155. Groups, subgroups, group homomorphisms, Lagrange’s Theorem, and the Fundamental Theorem of Group Homomorphisms.

MATH 5112. Introduction to Abstract Algebra 2 (3-0-3) Prerequisite: MATH 5111. Rings, integral domains, and fields.

MATH 5115. Linear Algebra (3-0-3) Prerequisites: MATH 2115 and MATH 5111. Linear transformations and vector spaces over various fields.

MATH 5116. Number Theory (3-0-3) Prerequisite: MATH 2155. Congruences, algebraic number fields, and prime number theorems.

MATH 5135. College Geometry (3-0-3) Prerequisite: MATH 1132. Axiomatic development of plane geometry and discussion of non-Euclidean geometry.

MATH 5151. Introduction to Real Analysis 1 (3-0-3) Prerequisite: MATH 2155. Topology of Euclidean spaces, sequences, limits of sequences, convergent sequences, monotone sequences, Cauchy sequences, limits of functions, continuous functions, the derivative, the mean value theorem, L’Hospitals’s rule, and Taylor’s theorem.

MATH 5152. Introduction to Real Analysis 2 (3-0-3) Prerequisite: MATH 5151. The Riemann Integral, the properties of the Riemann Integral, the Fundamental Theorem of Calculus, Infinite Series, convergence of infinite series, convergence tests, power series, sequences and infinite series of functions.

MATH 5165. Numerical Analysis (3-0-3) Prerequisites: MATH 1132, MATH 2115, and CPSC 1301. Use of computers to solve mathematical problems. Topics may include root finding, interpolation, numerical differentiation and integration, solutions to initial value problems in ordinary differential equations, and direct and iterative methods for solving linear systems. Error analysis. Use of appropriate software and technology.

MATH 5166. Linear Programming and Game Theory (3-0-3) Prerequisites: MATH 2115 and MATH 2175. Linear programming, simplex and interior point methods, duality and sensitivity. Game theory, two- and n-person games, utility theory, solution concepts. Applications may be included from anthropology, biology, business, economics, nutrition, politics, psychology or other areas. Computer technology will be used.

MATH 5175. Mathematical Statistics (3-0-3) Prerequisite: MATH 2175. Statistical inference, estimation, tests of statistical hypotheses, multivariate distributions, linear regression. Appropriate computational devices and statistical software will be used.

MATH 5176. Statistical Design and Analysis of Experiments (3-0-3) Prerequisite: MATH 2175. Completely randomized designs, treatment comparisons, diagnosing agreement between the data and the model, experiments to study variances, factorial treatment design and applications. Appropriate statistical software will be used.

MATH 5177. Applied Regression Analysis (3-0-3) Prerequisite: MATH 2175. Simple and multiple regression, transformation of variables, diagnostic procedures, analysis of variance and residuals, comparison of two multiple regression models, calibration and regulation for linear regression, linear splines, subset analysis and variable selection, nonlinear regression. Appropriate statistical software will be used.

MATH 5185. History of Mathematics (3-0-3) Prerequisite: MATH 1132. This course is designed to acquaint the student with the development of the discipline of mathematics in various cultures from antiquity to modern times. Special emphasis will be given to the evolutionary and Multicultural character of the principal ideas of modern mathematics.

MATH 5555. Selected Topics in Mathematics (3-0-3) Prerequisite: MATH 2155. Topics for this course will vary. May be repeated for credit with consent of the advisor and if topics are different.

MATH 6505. Selected Topics in Mathematics for Teachers (3-0-3) Prerequisite: Approval of Department Chair. Topics will be suitable for elementary and middle school teachers. Mathematics majors may not receive credit for this course.

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Last Updated: 2/1/11